A design of a Bragg reflector for a Raman FEL is described. It is shown that mode conversion occurs whenever the axial wavenumbers of the two modes fulfil the Bragg condition. With a constant ripple of the corrugation it is shown that the reflected radiation also contains higher order modes, assuming that the incident radiation consists only of a TE11 mode. The mode purity can be increased by increasing the length of the reflector at the expense of a smaller reflection bandwidth. A more flexible method is by applying a Hamming window to the corrugation of the reflector. Contributions of other modes to the reflected radiation can in that case be neglected. The reflector will be installed in a Raman laser to be able to compare the amplifier with the oscillator configuration. Therefore some preliminary results are also presented about the start-up of the Raman laser.